Answer
$\dfrac{9}{4}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the given expression, $
\left( \dfrac{2}{3} \right)^{-2}
,$ use the laws of exponents.
$\bf{\text{Solution Details:}}$
Using the Power of a Quotient Rule of the laws of exponents, which is given by $\left( \dfrac{x^m}{y^n} \right)^p=\dfrac{x^{mp}}{y^{np}},$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
\left( \dfrac{2}{3} \right)^{-2}
\\\\=
\dfrac{2^{-2}}{3^{-2}}
.\end{array}
Using the Negative Exponent Rule of the laws of exponents, which states that $x^{-m}=\dfrac{1}{x^m}$ or $\dfrac{1}{x^{-m}}=x^m,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{2^{-2}}{3^{-2}}
\\\\=
\dfrac{3^{2}}{2^{2}}
\\\\=
\dfrac{9}{4}
.\end{array}
